by PART V. Including Ratio and the Progressions. EXERCISE LXI. 1. IF a=1, b=2, c=-3, find the value of {a2b+5bc2-b2 (a−c)} {a+(b-c)} 2a-(c-263) 2. Divide a2 (b+c+2)+2(ab+ac) (b+c+2)-b-c-2 4. A dealer bought a horse for a certain number of pounds, and having resold it for £119, gained as much per cent. as the horse cost him: find the price of the horse. 6. Find the square root of 25x+10y √x+y2+10√x+2y+1. 7. If a b c d, prove that a2b3ac2: b3 - 3ad2=a2+5c2: b2+5d2. 8. Find the sum of 21 terms of an A. P. whose first and fourth terms are 4 and 13 respectively. EXERCISE LXII. 1. Resolve into factors: (1) 2x+3x2y+2x+3y. (2) 39x2-7x-22. 2. A and B distribute ten guineas each among the poor; Α relieves six more people than B, but B gives to each person four shillings more than A does: how many does each relieve? 5+3√8-7√6+3 √24 −√√/31 −10 √6. 1 У varies inversely as x-y, shew that x2+y2 varies 8. Insert n arithmetic means between a and b, and find the sum of the series thus formed. H. A. E. 4 7. If a+b, b+c, c+a are in continued proportion, prove that a+b, b+c, c-a, a-b are proportionals. 8. A man buys a shilling's worth of eggs, but having broken four they cost him each one farthing more than the market price : what is the market price per dozen? 2. A number of two digits bears the ratio of 7 4 to the number formed by inverting the digits. If the sum of the numbers is 66, find them. = 3104. 3. Solve (1) 3x3+x6 (2) 9x-3x2+4√√/x2−3x+5=11. 4. Resolve into factors: (1) 6(z−1)+5. (2) (α2 -1) x2 + (3α − 1) x + a − a2. 5. If x+y=u, xy=v, express x4+y4 in terms of u and v. 7. The sum of three terms of a harmonic series is 12, and 8. If x varies as the sum of the cubes of two quantities y and z whose sum is constant, find the value of x when y = 2, it being given that when x=3, y=3, and z=3. EXERCISE LXV. 1. Find the H. C. F. and L. C. M. of 39x2 - 178x+39, 39x2–184x+65, 27x2-114x – 13. |